Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BCA$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle ACB \cong \angle BDE$ $, \ $ $ \overline{BC} \cong \overline{BD}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ $ \angle ABC \cong \angle CFE$ $, \ $ and $\ $ $ \overline{AB} \cong \overline{EF}$ Proof $ \triangle BDE \cong \triangle BCA$ because ASA $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \angle CBE \cong \angle BED$ because alternate interior angles are equal $ \overline{AD} \cong \overline{CF}$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BCA$ because SAS $ \triangle BCE \cong \triangle BCA$ because SSS
Answer: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{CF} \cong \overline{AD}$ is the first wrong statement.